4. Complete the table below by solving each equation algebraically (expressing both sides with the same...

Transcribed Image Text:

4. Complete the table below by solving each equation algebraically (expressing both sides with the same base) and graphically (using technology). b. 9 = 27 Algebraically (2 marks) a. Algebraically (2 marks) 216 Graphically (1 mark) y = Y/ Coordinates of intersection U Solution X = Graphically (1 mark) Y = 9/= Coordinates of intersection Solution X = C. 5 = 254 Algebraically (2 marks) Graphically (1 mark) y = 1/ = Coordinates of intersection Solution X = (01) (a) Define the term "A is a o-algebra of subsets of a set X". (b) Let Abe a a- algebra of subsets of a set X and let Y be an arbitrary subset of X. Let B= (An Y: A A). Show that B is a o- algebra of subsets of Y. (e) Show that, if A, is a o- algebra for each a in some non- empty index set 1, then A acl A is a o-algebra. (d) Let f: XY be a function and B is a o- algebra of subset of Y. Then show that f(B) is a o-algebra on X. 4. Complete the table below by solving each equation algebraically (expressing both sides with the same base) and graphically (using technology). b. 9 = 27 Algebraically (2 marks) a. Algebraically (2 marks) 216 Graphically (1 mark) y = Y/ Coordinates of intersection U Solution X = Graphically (1 mark) Y = 9/= Coordinates of intersection Solution X = C. 5 = 254 Algebraically (2 marks) Graphically (1 mark) y = 1/ = Coordinates of intersection Solution X = (01) (a) Define the term "A is a o-algebra of subsets of a set X". (b) Let Abe a a- algebra of subsets of a set X and let Y be an arbitrary subset of X. Let B= (An Y: A A). Show that B is a o- algebra of subsets of Y. (e) Show that, if A, is a o- algebra for each a in some non- empty index set 1, then A acl A is a o-algebra. (d) Let f: XY be a function and B is a o- algebra of subset of Y. Then show that f(B) is a o-algebra on X.